Hyperbolic (1,2)-knots in S^3 with crosscap number two and tunnel number one
Geometric Topology
2008-12-17 v1
Abstract
A knot in S^3 is said to have crosscap number two if it bounds a once-punctured Klein bottle but not a Moebius band. In this paper we give a method of constructing crosscap number two hyperbolic (1,2)-knots with tunnel number one which are neither 2-bridge nor (1,1)-knots. An explicit infinite family of such knots is discussed in detail.
Cite
@article{arxiv.0812.3086,
title = {Hyperbolic (1,2)-knots in S^3 with crosscap number two and tunnel number one},
author = {Luis G. Valdez-Sanchez and Enrique Ramirez-Losada},
journal= {arXiv preprint arXiv:0812.3086},
year = {2008}
}
Comments
31 pages, 11 figures. To appear in Topology and its Applications (2008)